Last updated at Feb. 25, 2017 by Teachoo

Transcript

Ex 12.2, 5 In a circle of radius 21 cm, an arc subtends an angle of 60ยฐ at the centre. Find: the length of the arc Length of Arc APB = ๐/360ร(2๐๐) = (60ยฐ)/(360ยฐ)ร2ร22/7ร21 = 1/6ร2ร22/7ร21 = 22 cm Ex 12.2, 5 In a circle of radius 21 cm, an arc subtends an angle of 60ยฐ at the centre. Find: (ii) area of the sector formed by the arc Area of sector OAPB = ๐/360ร๐๐2 = 60/360ร22/7ร21ร21 = 1/6ร22/7ร21ร21 = 1/6ร22ร3ร21 = 231 cm2 Ex 12.2, 5 In a circle of radius 21 cm, an arc subtends an angle of 60ยฐ at the centre. Find: (iii) area of segment formed by the corresponding chord Area of segment APB = Area of sector OAPB โ Area of ฮOAB From last part, Area of sector OAPB = 231 cm2 Finding area of ฮ AOB Area ฮ AOB = 1/2 ร Base ร Height We draw OM โฅ AB โด โ OMB = โ OMA = 90ยฐ In ฮ OMA & ฮ OMB โ OMA = โ OMB OA = OB OM = OM โด ฮ OMA โ ฮ OMB โ โ AOM = โ BOM โด โ AOM = โ BOM = 1/2 โ BOA โ โ AOM = โ BOM = 1/2 ร 60ยฐ = 30ยฐ Also, since ฮ OMB โ ฮ OMA โด BM = AM โ BM = AM = 1/2 AB From (1) AM = 1/2AB 2AM = AB AB = 2AM Putting value of AM AB = 2 ร 21/2 AB = 21 Now, Area of ฮ AOB = 1/2 ร Base ร Height = 1/2 ร AB ร OM = 1/2 ร 21 ร โ3/2 ร 21 = (441โ3)/4 cm2 Area of segment APB = Area of sector OAPB โ Area of ฮOAB = (231 โ 441/4 โ3) cm2

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.